Unlocking the Standard Model. III. 2 Generations of quarks : calculating the Cabibbo angle

TL;DR

This paper derives a formula for the Cabibbo angle by extending the Higgs sector in the Standard Model to include all scalar and pseudoscalar states for two quark generations, linking it to meson masses.

Contribution

It introduces a maximal extension of the Higgs sector to calculate the Cabibbo angle based on meson mass ratios, providing a novel theoretical approach.

Findings

Derived an explicit formula for the Cabibbo angle.

Connected the angle to meson mass ratios.

Provided an approximation formula involving meson masses.

Abstract

Maximally extending the Higgs sector of the Glashow-Salam-Weinberg model by including all scalar and pseudoscalar J=0 states expected for 2 generations of quarks, I demonstrate that the Cabibbo angle is given by tan^2(theta_c) = (1/m_K^2-1/m_D^2)/(1/m_\pi^2-1/m_{D_s}^2) \approx (m_\pi^2 /m_K^2)(1-m_K^2/m_D^2 + m_\pi^2/m_{D_s}^2).